Hubbard- U calculations for Cu from first-principle Wannier functions

We present first-principles calculations of optimally localized Wannier functions for Cu and use these for an ab initio determination of Hubbard (Coulomb) matrix elements. We use a standard linearized muffin-tin orbital calculation in the atomic-sphere approximation to calculate Bloch functions, and from these determine maximally localized Wannier functions using a method proposed by Marzari and Vanderbilt. The resulting functions were highly localized, with greater than 89% of the norm of the function within the central site for the occupied Wannier states. Two methods for calculating Coulomb matrix elements from Wannier functions are presented and applied to fcc Cu. For the unscreened on-site Hubbard U for the Cu 3d bands, we have obtained about 25 eV. These results are also compared with results obtained from a constrained local-density approximation calculation.